Improved colored noise handling in Kalman Filter-based speech enhancement algorithms

Transcription

1 Improved colored noise handling in Kalman Filter-based speech enhancement algorithms F. Mustière, M. Bolić, M. Bouchard Ottawa University May 5 th 2008

2 Outline Outline 1 White and traditional colored noise handling 2 Proposed colored noise handling 3 Simulation results 4 Conclusions

3 White and traditional colored noise handling Current Topic 1 White and traditional colored noise handling 2 Proposed colored noise handling 3 Simulation results 4 Conclusions

4 White and traditional colored noise handling Kalman Filter based speech enhancement Model-based enhancement Speech modelled as autoregression Problem formulated by state-space equations Fairly large and established family of algorithms

5 White and traditional colored noise handling State-space model, white observation noise Time varying autoregressive model: p clean signal x(n) = a k (n)x(n k) + σ e (n)e(n) k=1 measurement signal y(n) = x(n) + σ v (n)v(n) In matrix form: clean signal measurement signal x(n) = A k (n)x(n k) + G(n)e(n) y(n) = Cx(n) + σ v (n)v(n)

6 White and traditional colored noise handling Traditional colored noise handling Traditional way of augmenting system: clean signal noise signal measurement equation x(n) = A k (n)x(n k) + G(n)e(n) n(n) = B k (n)n(n k) + H(n)v(n) y(n) = Cx(n) + Dn(n) with A, B respectively of size p p, q q.

7 White and traditional colored noise handling Traditional colored noise handling Remarks: Redundancy in the (large) state-vector Noise-free observation equation potentially very small error covariance matrix potential stability problems Does not reduce to white noise state-space equations for 0 AR order

8 Proposed colored noise handling Current Topic 1 White and traditional colored noise handling 2 Proposed colored noise handling 3 Simulation results 4 Conclusions

9 Proposed colored noise handling Rewriting of the state-space equations: Traditional (again) clean signal noise signal measurement equation x(n) = A k (n)x(n k) + G(n)e(n) n(n) = B k (n)n(n k) + H(n)v(n) y(n) = Cx(n) + Dn(n) Proposed clean signal measurement equation x(n) = A k (n)x(n k) + G(n)e(n) y(n) = Cx(n) + b T k (n)y(n 1) + σ v (n)v(n) with y(n) a trail of measurements of size q, and C = [1, b T k (n), ].

10 Proposed colored noise handling Apparent advantages Remarks Smaller state-vector, no redundancy Less computations, less memory required No noise-free measurement equation Naturally reduces to white noise state-space model

11 Proposed colored noise handling Gain in efficiency Parameters Regular Proposed M s M n Table: Examples of computational load for both types of KFs. 1 M s = speech AR order M n = noise AR order 1 Detailed complexity analysis available in paper

12 Simulation results Current Topic 1 White and traditional colored noise handling 2 Proposed colored noise handling 3 Simulation results 4 Conclusions

13 Simulation results Test algorithms and conditions Algorithms used 1 Plain/Classic Kalman Filter, true AR parameters measured from speech and noise signals, PKF 2 Rao-Blackwellized Particle Filter (Vermaak, 2002), and true AR parameters measured from noise signal, RBPF 3 KF with EM algorithm (Gannot, 1998) updating speech AR parameters, and true AR parameters measured from noise signal, KEM

14 Simulation results Results Type of algorithm Quality measure Regular Proposed Noisy speech PlainKF KEM RBPF Cafeteria noise SNR 3.57 wpesq 1.33 SNR wpesq SNR wpesq SNR wpesq Table: Experimental results in cafeteria noise

15 Simulation results Results Type of algorithm Quality measure Regular Proposed Noisy speech PlainKF KEM RBPF Stationary hoth noise SNR 2.96 wpesq 1.29 SNR wpesq SNR wpesq SNR wpesq Table: Experimental results in hoth noise

16 Conclusions Current Topic 1 White and traditional colored noise handling 2 Proposed colored noise handling 3 Simulation results 4 Conclusions

17 Conclusions Conclusions More efficient implementation based on simple rewriting of state-space models Equivalent (in some cases better) results No apparent disadvantage Ready to be used as part of any state-space based speech enhancement algorithm

18 Conclusions Questions? Frédéric Mustière

19 Conclusions Regular KF iteration KF Step, update of [x, P 1 ] 1. P t1 = FP 1 F T + HH T 2. t 1 = DP t1 D T 3. x t = Fx 4. y 1 = Dx t 5. J 1 = P t1 D T t x = x t + J 1 (z y 1 ) 7. P 1 = P t1 J 1 DP t1 x k = F k x k 1 + H k η k (1) z k = Dx k (2)

20 Conclusions Proposed KF iteration s k = A k s k 1 + G k w k (3) z k = C k s k + b k T z k 1 + σ v,k v k (4) where C k = [ 1, b T k, 0 ] 1 M s M n 1 KF Step, update of [s, P 2 ] 1. P t2 = AP 2 A T + GG T 2. t 2 = CP CT t2 + σv 2 3. s t = As 4. y 2 = Cs t + u 5. J 2 = P CT t2 t s = s t + J 2 (z y 2 ) 7. P 2 = P t2 J 2 CPt2